Finite Group Databasebeta

← Group #13165499

Character table — Group #13165499

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222333344444444888888881212121212121212121212121212121212121212181818181818242424242424242424242424363636363636363636363636363636363636545454545454
order12223666444433666666336666662244666612121212121212121212121244888866666612121212121244441212121212121212121224242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-11-1-1-1-111111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111
χ511111111-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ611111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-111111-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91-11-11-1-11ii−i−i111-1-1-11-1111-11-1-1-11-1i−i11-1-1ii−i−iii−i−iii−i−i-11ii−i−i1-111-1-1i−iii−i−ii−i1-1111-1-1ii−i−i-1ii−i−ii−i11-1-1
χ101-11-11-1-11ii−i−i111-1-1-11-1111-11-1-1-11-1−ii11-1-1ii−i−i−i−iiiii−i−i-11−i−iii1-111-1-1−ii−i−iiii−i-111-1-111ii−i−i-1−i−iiii−i-1-111
χ111-11-11-1-11ii−i−i111-1-1-11-1111-11-1-1-1-11i−i-1-111ii−i−iii−i−iii−i−i-11−i−iii-11-1-111i−iii−i−i−ii1-1111-1-1−i−iii-1−i−iiii−i-1-111
χ121-11-11-1-11ii−i−i111-1-1-11-1111-11-1-1-1-11−ii-1-111ii−i−i−i−iiiii−i−i-11ii−i−i-11-1-111−ii−i−iii−ii-111-1-111−i−iii-1ii−i−ii−i11-1-1
χ131-11-11-1-11−i−iii111-1-1-11-1111-11-1-1-11-1i−i11-1-1−i−iiiii−i−i−i−iii-11ii−i−i1-111-1-1i−iii−i−i−ii-111-1-111−i−iii-1ii−i−i−ii-1-111
χ141-11-11-1-11−i−iii111-1-1-11-1111-11-1-1-11-1−ii11-1-1−i−iii−i−iii−i−iii-11−i−iii1-111-1-1−ii−i−iii−ii1-1111-1-1−i−iii-1−i−iii−ii11-1-1
χ151-11-11-1-11−i−iii111-1-1-11-1111-11-1-1-1-11i−i-1-111−i−iiiii−i−i−i−iii-11−i−iii-11-1-111i−iii−i−ii−i-111-1-111ii−i−i-1−i−iii−ii11-1-1
χ161-11-11-1-11−i−iii111-1-1-11-1111-11-1-1-1-11−ii-1-111−i−iii−i−iii−i−iii-11ii−i−i-11-1-111−ii−i−iiii−i1-1111-1-1ii−i−i-1ii−i−i−ii-1-111
χ17222222222222222222222222222200000000222200002222-2-200000000000000000000-200000000-20000-2-20000
χ1822222222-2-2-2-2222222222222222200000000-2-2-2-20000-2-2-2-2-2-200000000000000000000-200000000-20000220000
χ192222-1-1-1-1000022222222-1-1-1-1-1-1-1-122222222000022220000222222-1-1-1-1-1-1-1-1-1-1-1-10000-100000000-1-1-1-1-1000000
χ202222-1-1-1-1000022222222-1-1-1-1-1-1-1-122-2-222220000-2-2-2-2000022-2-2-2-2-1-1-1-1-1-11111110000-100000000-11111000000
χ212222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-222-2-2-2-200002222000022-2-2-2-2111111-1-1-1-1-1-10000-100000000-11111000000
χ222222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000-2-2-2-200002222221111111111110000-100000000-1-1-1-1-1000000
χ2322-2-222-2-22-22-222-2-22-2-2222-22-22-2-2000000002-22-200002-22-200−i2i2−i2i200000000000000000000000000−i2i2−i2i200−i2i2−i2i2
χ2422-2-222-2-22-22-222-2-22-2-2222-22-22-2-2000000002-22-200002-22-200i2−i2i2−i200000000000000000000000000i2−i2i2−i200i2−i2i2−i2
χ2522-2-222-2-2-22-2222-2-22-2-2222-22-22-2-200000000-22-220000-22-2200−i2i2−i2i200000000000000000000000000−i2i2−i2i200i2−i2i2−i2
χ2622-2-222-2-2-22-2222-2-22-2-2222-22-22-2-200000000-22-220000-22-2200i2−i2i2−i200000000000000000000000000i2−i2i2−i200−i2i2−i2i2
χ272-22-22-2-222i2i−2i−2i222-2-2-22-2222-22-2-2-2000000002i2i−2i−2i00002i2i−2i−2i2-200000000000000000000-20000000020000−2i2i0000
χ282-22-22-2-22−2i−2i2i2i222-2-2-22-2222-22-2-2-200000000−2i−2i2i2i0000−2i−2i2i2i2-200000000000000000000-200000000200002i−2i0000
χ292-22-2-111-10000222-2-2-22-2-1-1-11-11112-22i−2i22-2-200002i2i−2i−2i0000-222i2i−2i−2i-11-1-111−ii−i−iii0000-1000000001−i−iii000000
χ302-22-2-111-10000222-2-2-22-2-1-1-11-11112-2−2i2i22-2-20000−2i−2i2i2i0000-22−2i−2i2i2i-11-1-111i−iii−i−i0000-1000000001ii−i−i000000
χ312-22-2-111-10000222-2-2-22-2-1-1-11-1111-222i−2i-2-22200002i2i−2i−2i0000-22−2i−2i2i2i1-111-1-1−ii−i−iii0000-1000000001ii−i−i000000
χ322-22-2-111-10000222-2-2-22-2-1-1-11-1111-22−2i2i-2-2220000−2i−2i2i2i0000-222i2i−2i−2i1-111-1-1i−iii−i−i0000-1000000001−i−iii000000
χ332-2-222-22-22i−2i−2i2i22-22-22-2-222-2-2-2-222000000002i−2i−2i2i00002i−2i−2i2i002−2−22000000000000000000000000002−2−2200−i2i2i2−i2
χ342-2-222-22-22i−2i−2i2i22-22-22-2-222-2-2-2-222000000002i−2i−2i2i00002i−2i−2i2i00−222−200000000000000000000000000−222−200i2−i2−i2i2
χ352-2-222-22-2−2i2i2i−2i22-22-22-2-222-2-2-2-22200000000−2i2i2i−2i0000−2i2i2i−2i002−2−22000000000000000000000000002−2−2200i2−i2−i2i2
χ362-2-222-22-2−2i2i2i−2i22-22-22-2-222-2-2-2-22200000000−2i2i2i−2i0000−2i2i2i−2i00−222−200000000000000000000000000−222−200−i2i2i2−i2
χ374444444444441-2-2-2111-21-211-2-2-21002200001111-1-1-1-1-2-2-2-200000000000022-1-1-1-100220-1-1-1-1000000000000000
χ384444444444441-2-2-2111-21-211-2-2-2100-2-2000011111111-2-2-2-2000000000000-2-2111100-2-201111000000000000000
χ39444444444444-2111-2-2-21-21-2-2111-22200-1-1-1-1-2-2-2-20000111100000022-1-1-1-1000000220000000-1-1-1-100000000000
χ40444444444444-2111-2-2-21-21-2-2111-2-2-2001111-2-2-2-200001111000000-2-21111000000-2-20000000111100000000000
χ4144444444-4-4-4-41-2-2-2111-21-211-2-2-2100220000-1-1-1-1-1-1-1-1222200000000000022-1-1-1-100-2-201111000000000000000
χ4244444444-4-4-4-41-2-2-2111-21-211-2-2-2100-2-20000-1-1-1-111112222000000000000-2-2111100220-1-1-1-1000000000000000
χ4344444444-4-4-4-4-2111-2-2-21-21-2-2111-22200-1-1-1-122220000-1-1-1-100000022-1-1-1-1000000-2-20000000111100000000000
χ4444444444-4-4-4-4-2111-2-2-21-21-2-2111-2-2-200111122220000-1-1-1-1000000-2-21111000000220000000-1-1-1-100000000000
χ454444-2-2-2-2000044444444-2-2-2-2-2-2-2-200000000000000000000-4-40000000000000000000020000000020000000000
χ4644-4-444-4-44-44-41-2221-1-1-21-2-112-22-1000000001-11-13−33−3-22-22000000000000003−33−3000003−33−3000000000000000
χ4744-4-444-4-44-44-41-2221-1-1-21-2-112-22-1000000001-11-1−33−33-22-2200000000000000−33−3300000−33−33000000000000000
χ4844-4-444-4-44-44-4-21-1-1-2221-212-2-11-120000−i3i3−i3i3-22-2200001-11-100000000−i3i3−i3i3000000000000000−i3i3−i3i300000000000
χ4944-4-444-4-44-44-4-21-1-1-2221-212-2-11-120000i3−i3i3−i3-22-2200001-11-100000000i3−i3i3−i3000000000000000i3−i3i3−i300000000000
χ5044-4-444-4-4-44-441-2221-1-1-21-2-112-22-100000000-11-113−33−32-22-2000000000000003−33−300000−33−33000000000000000
χ5144-4-444-4-4-44-441-2221-1-1-21-2-112-22-100000000-11-11−33−332-22-200000000000000−33−33000003−33−3000000000000000
χ5244-4-444-4-4-44-44-21-1-1-2221-212-2-11-120000−i3i3−i3i32-22-20000-11-1100000000−i3i3−i3i3000000000000000i3−i3i3−i300000000000
χ5344-4-444-4-4-44-44-21-1-1-2221-212-2-11-120000i3−i3i3−i32-22-20000-11-1100000000i3−i3i3−i3000000000000000−i3i3−i3i300000000000
χ5444-4-4-2-222000044-4-44-4-44-2-22-22-2220000000000000000000000−2i22i2−2i22i200000000000000000000000000i2−i2i2−i2000000
χ5544-4-4-2-222000044-4-44-4-44-2-22-22-22200000000000000000000002i2−2i22i2−2i200000000000000000000000000−i2i2−i2i2000000
χ564-44-44-4-444i4i−4i−4i1-2-22-1-1121-21-1-222-1002i−2i0000ii−i−i−i−iii−2i−2i2i2i0000000000002i−2i−i−iii002-20-1-111000000000000000
χ574-44-44-4-444i4i−4i−4i1-2-22-1-1121-21-1-222-100−2i2i0000ii−i−iii−i−i−2i−2i2i2i000000000000−2i2iii−i−i00-22011-1-1000000000000000
χ584-44-44-4-444i4i−4i−4i-211-122-2-1-21-221-1-122-200-1-111−2i−2i2i2i0000ii−i−i0000002-2-1-1110000002i−2i0000000−i−iii00000000000
χ594-44-44-4-444i4i−4i−4i-211-122-2-1-21-221-1-12-220011-1-1−2i−2i2i2i0000ii−i−i000000-2211-1-1000000−2i2i0000000ii−i−i00000000000
χ604-44-44-4-44−4i−4i4i4i1-2-22-1-1121-21-1-222-1002i−2i0000−i−iii−i−iii2i2i−2i−2i0000000000002i−2i−i−iii00-22011-1-1000000000000000
χ614-44-44-4-44−4i−4i4i4i1-2-22-1-1121-21-1-222-100−2i2i0000−i−iiiii−i−i2i2i−2i−2i000000000000−2i2iii−i−i002-20-1-111000000000000000
χ624-44-44-4-44−4i−4i4i4i-211-122-2-1-21-221-1-122-200-1-1112i2i−2i−2i0000−i−iii0000002-2-1-111000000−2i2i0000000ii−i−i00000000000
χ634-44-44-4-44−4i−4i4i4i-211-122-2-1-21-221-1-12-220011-1-12i2i−2i−2i0000−i−iii000000-2211-1-10000002i−2i0000000−i−iii00000000000
χ644-44-4-222-20000444-4-4-44-4-2-2-22-2222000000000000000000004-400000000000000000000200000000-20000000000
χ654-4-444-44-44i−4i−4i4i1-22-2-11-121-2-1-122-2100000000i−i−ii−i3i3i3−i3−2i2i2i−2i00000000000000−i3i3i3−i300000−333−3000000000000000
χ664-4-444-44-44i−4i−4i4i1-22-2-11-121-2-1-122-2100000000i−i−iii3−i3−i3i3−2i2i2i−2i00000000000000i3−i3−i3i3000003−3−33000000000000000
χ674-4-444-44-44i−4i−4i4i-21-112-22-1-2122-1-11-20000−i3i3i3−i3−2i2i2i−2i0000i−i−ii00000000−i3i3i3−i30000000000000003−3−3300000000000
χ684-4-444-44-44i−4i−4i4i-21-112-22-1-2122-1-11-20000i3−i3−i3i3−2i2i2i−2i0000i−i−ii00000000i3−i3−i3i3000000000000000−333−300000000000
χ694-4-444-44-4−4i4i4i−4i1-22-2-11-121-2-1-122-2100000000−iii−i−i3i3i3−i32i−2i−2i2i00000000000000−i3i3i3−i3000003−3−33000000000000000
χ704-4-444-44-4−4i4i4i−4i1-22-2-11-121-2-1-122-2100000000−iii−ii3−i3−i3i32i−2i−2i2i00000000000000i3−i3−i3i300000−333−3000000000000000
χ714-4-444-44-4−4i4i4i−4i-21-112-22-1-2122-1-11-20000−i3i3i3−i32i−2i−2i2i0000−iii−i00000000−i3i3i3−i3000000000000000−333−300000000000
χ724-4-444-44-4−4i4i4i−4i-21-112-22-1-2122-1-11-20000i3−i3−i3i32i−2i−2i2i0000−iii−i00000000i3−i3−i3i30000000000000003−3−3300000000000
χ734-4-44-22-22000044-44-44-4-4-2-22222-2-2000000000000000000000022−22−222200000000000000000000000000−222−2000000
χ744-4-44-22-22000044-44-44-4-4-2-22222-2-20000000000000000000000−222222−22000000000000000000000000002−2−22000000
χ758888-4-4-4-400002-4-4-4222-4-12-1-1222-1004400000000-2-2-2-20000000000000000-2-21111000000000000000000000000
χ768888-4-4-4-400002-4-4-4222-4-12-1-1222-100-4-4000000002222000000000000000022-1-1-1-1000000000000000000000000
χ778888-4-4-4-40000-4222-4-4-422-122-1-1-124400-2-2-2-2000000000000000000-2-21111000000000000000000000000000000
χ788888-4-4-4-40000-4222-4-4-422-122-1-1-12-4-400222200000000000000000022-1-1-1-1000000000000000000000000000000
χ7988-8-8-4-44400002-4442-2-2-4-121-1-22-2100000000000023−2323−23000000000000000000−33−33000000000000000000000000
χ8088-8-8-4-44400002-4442-2-2-4-121-1-22-21000000000000−2323−23230000000000000000003−33−3000000000000000000000000
χ8188-8-8-4-4440000-42-2-2-44422-1-221-11-20000−2i32i3−2i32i300000000000000000000i3−i3i3−i3000000000000000000000000000000
χ8288-8-8-4-4440000-42-2-2-44422-1-221-11-200002i3−2i32i3−2i300000000000000000000−i3i3−i3i3000000000000000000000000000000
χ838-88-8-444-400002-4-44-2-224-12-112-2-21004i−4i00000000−2i−2i2i2i0000000000000000−2i2iii−i−i000000000000000000000000
χ848-88-8-444-400002-4-44-2-224-12-112-2-2100−4i4i000000002i2i−2i−2i00000000000000002i−2i−i−iii000000000000000000000000
χ858-88-8-444-40000-422-244-4-22-12-2-111-24-400-2-222000000000000000000-2211-1-1000000000000000000000000000000
χ868-88-8-444-40000-422-244-4-22-12-2-111-2-440022-2-20000000000000000002-2-1-111000000000000000000000000000000
χ878-8-88-44-4400002-44-4-22-24-1211-2-22-1000000000000−2i32i32i3−2i3000000000000000000i3−i3−i3i3000000000000000000000000
χ888-8-88-44-4400002-44-4-22-24-1211-2-22-10000000000002i3−2i3−2i32i3000000000000000000−i3i3i3−i3000000000000000000000000
χ898-8-88-44-440000-42-224-44-22-1-2-211-120000−2i32i32i3−2i300000000000000000000i3−i3−i3i3000000000000000000000000000000
χ908-8-88-44-440000-42-224-44-22-1-2-211-1200002i3−2i3−2i32i300000000000000000000−i3i3i3−i3000000000000000000000000000000

Here i is the imaginary unit (i² = −1).